School of Mathematics
School of Mathematics
Module MA1111 - Linear algebra I
2011-12 (
JF Mathematics, JF Theoretical Physics & JF Two-subject Moderatorship
)
Lecturer: Prof. P. Karageorgis
Requirements/prerequisites:
Duration: Michaelmas term, 11 weeks
Number of lectures per week: 3 lectures including tutorials per week
Assessment:
Homework assignments will be due every Thursday.
20% homework, 80% final exam (based on homework and tutorials).
ECTS credits: 5
End-of-year Examination:
2 hour end of year examination.
Description:
We will cover the following topics, yet not necessarily in the order
listed.
- Lines, planes and vectors, dot and cross product.
- Linear systems, Gauss-Jordan elimination, reduced
row echelon
form.
- Matrix multiplication, elementary row operations,
inverse
matrix.
- Permutations, odd and even, determinants, transpose
matrix.
- Minors, cofactors, adjoint matrix, inverse matrix,
Cramer's
rule.
- Vector spaces, linear independence and span, bases
and
dimension.
- Linear operators, matrix of a linear operator with
respect to a
basis.
- Change of basis, transition matrix, conjugate
matrices.
Textbook
We will not follow any particular textbook. Two typical references
are
- Algebra by Michael Artin,
- Basic linear algebra by Blyth and Robertson.
Notes, homework assignments and solutions will be posted on the web
page
Learning
Outcomes:
On successful completion of this module, students will be able to:
- operate with vectors in dimensions 2 and 3, and apply vectors
to solve basic geometric problems;
- apply various standard methods (Gauss-Jordan elimination,
inverse matrices, Cramer's rule) to solve systems of simultaneous linear equations;
- compute the sign of a given permutation, and apply theorems
from the course to compute determinants of square matrices;
- demonstrate that a system of vectors forms a basis of the
given vector space, compute coordinates of given vectors relative to the given basis, and
calculate the matrix of a linear operator relative to the given bases;
- give examples of sets where some of the defining properties
of vectors, matrices, vector spaces, subspaces, and linear operators fail;
- identify the above linear algebra problems in various
settings (e.g. in the case of the vector space of polynomials, or the vector space of matrices of
given size), and apply methods of the course to solve those problems.
Oct 6, 2011
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On 6 Oct 2011, 15:43.